CHICAGO — Commonwealth Edison’s residential customers will see a 38 percent spike in their electricity bills beginning next month, just six months after the company raised rates to help pay for the costs of upgrading the power grid, the company said Wednesday.

The increase came after the Illinois Power Authority, which buys electricity on behalf of the northern Illinois utility, set the company’s per-kilowatt-hour costs at just over 7 ½ cents, up from 5 ½ cents in 2013, ComEd spokesman David O’Dowd told the (Arlington Heights) Daily Herald.

That means an average bill of $68 for about 655 kilowatts of electricity monthly, will rise to about $83 beginning June 1, O’Dowd said.

Power costs represent about two-thirds of a customer’s bill. The other portion is for distribution costs, which also have been rising.

The average bill increased by $5.50 per month in January after ComEd received permission from the Illinois Commerce Commission to collect an additional $340 million for distribution, largely to offset its cost to help modernize the electric grid.

Last month, ComEd asked for another distribution increase starting in January 2015. If approved, that increase would cost the average customer about $3 more per month, the company has said.

ComEd and downstate electricity provider Ameren are undertaking a 10-year, $3.2 billion project to modernize and “storm-harden” Illinois’ power grid to make it more efficient and reliable. That includes replacing aging cables and poles, and switching customers to wireless “smart meters.”